From: Neil Sklar <rp_mcmurphy@hotmail.com>
To: Teacher2Teacher Public Discussion
Date: 2008071023:06:07
Subject: partial products

Hi,

Put simply, the reason the zeros need to be inserted is to cause the
place values to line up correctly.

I teach this by physically decomposing one of the factors into partial
products, then adding the products together, as follows:

123 X 123 is equivalent to (120 X 100) + (120 X 20) + (120 X 3).

120 X 3 = 360

120 X 20 = (120 X 2 X 10) = 2400
120 X 2 = 240, and we can use the "trick" (though I prefer that
students understand the reasoning behind it) of inserting a 0 at the
end of the 240 to get 2400.

120 X 100 = (120 X 1 X 100) = 36000
120 X 1 = 120, and insert the two zeros to get 12000.

Then add 360 + 2400 + 360000.

If you do this to build understanding of concept before (or instead
of) teaching the 'standard algorithm,' students are far more likely to
understand that they need to insert the zeros so that the place values
will be aligned correctly.

Feel free to post or email me if you'd like more detail on how to
present this.

Good luck,
Neil

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